Internal problem ID [6815]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 83.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+4*x*diff(y(x),x)+(2+4*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x^{2}} c_{1}+c_{2} x \,{\mathrm e}^{-x^{2}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 20
DSolve[y''[x]+4*x*y'[x]+(2+4*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x^2} (c_2 x+c_1) \\ \end{align*}